On the thermodynamics consistency of Gurson’s model and its computational implications

Abstract

The aim of this paper is to investigate the thermodynamics consistency of Gurson’s model and notably its relation to the class of standard generalized materials. First, we briefly recall Gurson’s model in its original format and reanalyzed it in the thermodynamic framework of poroplasticity of saturated media. This allows to properly define the coupling between elasticity and plasticity and to demonstrate that Gurson’s model fits into the framework of generalized standard materials model, provided that the internal variables being the plastic strain and the Lagrangian plastic porosity (and not the Eulerian porosity as in the original Gurson model). In particular, by construction, the porosity evolution law is proved to be a full part of the thermodynamic formulation of the model with a generalized normality rule. The implications in terms of numerical implementation of Gurson’s model are then investigated; a new numerical scheme based on the time-implicit discretization of the Lagrangian porosity is notably proposed and discussed with respect to available algorithms.